[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 389 from proof inv-write (previous step)

VFS_PAGE_SIZE = n1 + (m0 + ino0) % VFS_PAGE_SIZE, files0[m] = mkfile(m1, md, # links(m, dirs), content0), of[fd] = mkfile(m, mode, m0), buf = mkbuf(VFS_PAGE_SIZE), err = ESUCCESS, ino = (m0 + ino0) % VFS_PAGE_SIZE, inode = mkinode(m, md, false, # links(m, dirs), 0, m1), n = min(m0 + n0 - m0 + ino0, n1), pageno = (m0 + ino0) / VFS_PAGE_SIZE, dom of < ino3, afs-cons(dirs, files0), afs-cons(dirs, files), of-cons(of, dirs, files0), of-cons(of, dirs, files), fd ∈ of, m ∈ files0, n0 ≤ # buf0, ino0 ≤ n0, ino0 ≤ # buf0, m0 + n0 ≥ m0 + ino0 ⊦ [afs_readpage#(inode, pageno, dirs, files, asynced; buf, err); if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then {buf := copy(buf0, ino0, buf, ino, n); afs_writepage#(inode, pageno, buf, dirs; err, files; asynced)}; if err = ESUCCESS then ino3 := ino0 + min(m0 + n0 - m0 + ino0, n1)] (of-cons(of, dirs, files) ∧ afs-cons(dirs, files)), VFS_PAGE_SIZE = 0, min(n0 - ino0, n1) = 0, n0 = 0, mode ≠ MODE_W ∧ mode ≠ MODE_RW, m1 % VFS_PAGE_SIZE ≠ 0 ∧ m1 / VFS_PAGE_SIZE ∈ content0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 390:
VFS_PAGE_SIZE = n1 + (m0 + ino0) % VFS_PAGE_SIZE, of[fd] = mkfile(m, mode, m0), files0[m] = mkfile(m1, md, # links(m, dirs), content0), buf = mkbuf(VFS_PAGE_SIZE), err = ESUCCESS, min(n0 - ino0, n1) ≠ 0, n0 ≠ 0, dom of < ino3, afs-cons(dirs, files), afs-cons(dirs, files0), of-cons(of, dirs, files), of-cons(of, dirs, files0), m ∈ files0, fd ∈ of, ino0 ≤ # buf0, n0 ≤ # buf0, ino0 ≤ n0 ⊦ [afs_readpage#(mkinode(m, md, false, # links(m, dirs), 0, m1), (m0 + ino0) / VFS_PAGE_SIZE, dirs, files, asynced; buf, err); if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then {buf := copy(buf0, ino0, buf, (m0 + ino0) % VFS_PAGE_SIZE, min(m0 + n0 - m0 + ino0, n1)); afs_writepage#(mkinode(m, md, false, # links(m, dirs), 0, m1), (m0 + ino0) / VFS_PAGE_SIZE, buf, dirs; err, files; asynced)}; if err = ESUCCESS then ino3 := ino0 + min(m0 + n0 - m0 + ino0, n1)] (of-cons(of, dirs, files) ∧ afs-cons(dirs, files)), m1 % VFS_PAGE_SIZE ≠ 0 ∧ m1 / VFS_PAGE_SIZE ∈ content0, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)